What is topology | What is isomorphism | Homomorphism | What is homeomorphism | Homeomorphic surface

[@mosesobinnafrancis5409]

I have never seen anybody teach topology like you sir. 100% visual. I love your videos. Thank you so much sir. Sir, I don't know if you can help me with how to transform semigroup to topology. Thanking you My mail [e-mail]

[@physicsforstudents]

Dear Moses, I am so touched by your words. Thank you for watching my videos. The topic that you have mentioned, I need to check. To be very honest, I never looked into it. I have noted your email id and you can write back to me at [e-mail]. I am also putting up those videos in a form of writing. One you can find here: www.academia.edu/s/8aebb89c07 Please do write to me and watch this channel as I am trying to bring up more interesting vidoes. Thank you once again.

[@LiyanasKeyboard]

Nice 👍👍👍🙂🙂🙂

[@dr.rajanikamble1620]

Thank you sir

[@physicsforstudents]

Welcome

[@vikashdhillon04]

thanks for this video

[@physicsforstudents]

Welcome ❤️❤️

[@hyperduality2838]

Injective is dual to surjective synthesizes bi-jective or isomorphism. Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic. "Always two there are" -- Yoda.

[@physicsforstudents]

Well said

[@hyperduality2838]

@@physicsforstudents Cheers! Topology is alot of fun. Subspace topology is dual to quotient topology. Homology is dual to co-homology. Galois groups are dual to modular forms -- group theory. Modular forms are dual to elliptic curves. Integration is dual to differentiation. Addition is dual to subtraction (additive inverses). Multiplication is dual to division (multiplicative inverses). All mathematical equations are dualities:- Y = X. Y is equal to X. Y is the same, similar, equivalent or dual to X. Y is dual to X. Points are dual to lines -- the principle of duality in geometry. Null homotopic implies contraction to a point and non null homotopic requires at least two points (duality) -- topology. Vectors are dual to co-vectors (forms). The inner product is dual to the cross product -- Maxwell's equations. etc.etc. There is a pattern of duality hardwired into mathematics, physics & philosophy. Duality: two equivalent descriptions of the same thing -- Leonard Susskind, physicist. Two sides of the same coin (heads, tails) -- duality. Space is dual to time -- Einstein. Time dilation is dual to length contraction -- Einstein, special relativity. Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. "All geometries are projective geometries" -- Arthur Cayley, mathematician. Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality). Gravitation is dual to acceleration -- Einstein. Gravitation or curvature is dual. Apples fall to the ground because they are conserving duality. Potential energy is dual to kinetic energy -- gravitational energy is dual. Spin up is dual to spin down, particles are dual to anti-particles -- the Dirac equation. Positive charge (positive numbers) is dual to negative charge (negative numbers) -- electric fields. North poles are dual to south poles -- magnetic fields. Electro is dual to magnetic -- electro-magnetic energy (light, photons) is dual. Energy is duality, duality is energy! Once you understand this pattern you can create new laws of physics:- Syntropy (prediction, projection) is dual to increasing entropy -- the 4th law of thermodynamics! Teleological physics (syntropy) is dual to non teleological physics (entropy). Certainty (predictability, syntropy) is dual to uncertainty (unpredictability, entropy) -- the Heisenberg certainty/uncertainty principle. Homo is dual to hetero, same is dual to different, homoosious is dual to heteroosious (Greek). Everything is made out of the same substance namely energy but comes in differing forms. Forms are dual to formlessness. Concepts are dual to percepts -- the mind duality of Immanuel Kant. "May the force (duality) be with you" -- Jedi teaching.

[@bakkamydestination]

👍👍👍 very useful ☺️...I got an idea of Topological spaces through ur videos..... excellent 👌

[@physicsforstudents]

Thank you very much for watching. Have you seen this video? I also have a separate video on Topology and Topological spaces. Here is the video kzbin.info/www/bejne/j6rSe2Oripyllck

[@bakkamydestination]

@@physicsforstudents ...I Saw this video first....I was really confused with Topology... but now I m comfort ....I also want to know about the convergence....can you help me

[@physicsforstudents]

@@bakkamydestination It is good to know that your confusion is now cleared. Convergence and divergence? Do you mean that ?

[@bakkamydestination]

@@physicsforstudents S..sir

[@nidafatima7740]

Keep it up 👍

[@physicsforstudents]

Thanks

[@soumitrapandit3444]

Hello sir, Really nice video, but I don't see how the two graphs at 6:51 are isomorphic as the vertice connections are not the same. Or do we not care about names?

[@physicsforstudents]

Yes you are right. The graphs are not isomorphic. However, the basic idea is to give the clarity of concepts....

[@scienceandmath-k9]

Nice sir

[@physicsforstudents]

Thank you 🙏